Wikipedia:Reference desk/Archives/Mathematics/2018 August 7

= August 7 =

Fourier series question
How do I get the Fourier series expansion for $$\text{cosec}^2 (nx)$$? I've tried doing the integrals with Mathematica, but they look unreasonably ugly.--Leon (talk) 13:06, 7 August 2018 (UTC)


 * It's been a while, but $$f(x) = \csc^2 x$$ is not a square-integrable function (over $$[0,2\pi]$$ say), so it doesn't have a Fourier series. –Deacon Vorbis (carbon &bull; videos) 14:57, 7 August 2018 (UTC)


 * Ah. Thanks.--Leon (talk) 15:42, 7 August 2018 (UTC)

Distance on an oblate spheroid
On a normal spheroid, the distance between two points along the surface is relatively trivial to compute. But is there a closed form solution for the same problem on an oblate spheroid like the earth? For the purposes of this, "closed form" can include elliptic integrals, and I have this feeling that will be necessary.--Jasper Deng (talk) 17:54, 7 August 2018 (UTC)


 * See Geodesics on an ellipsoid --catslash (talk) 19:28, 7 August 2018 (UTC)